1. Introduction

In this notebook, I examine the relationship between utterance fluency (UF) measures and L2 speaking anxiety, addressing the following three research questions (RQs):

In the following sections, I preprocess data, conduct preliminary analyses, and construct regression models.

The following code block loads R packages required for analyses.

pacman::p_load(
  tidyverse, here, skimr, psych, 
  PerformanceAnalytics, sjPlot, performance
)

2. Data Preprocess

This section tidies data. First of all, the following code block loads data of UF measures.

df_uf_raw <- read.csv(here("data", "processed", "uf_measures.csv"))

The current analysis focuses on the UF measures shown in Table 1.

Table 1. UF Dimension and Corresponding Measures

UF Dimension Measure
Speed Fluency (SF) Articulation Rate (AR)
Breakdown Fluency (BDF) Mid-Clause Pause Ratio (MCPR)
End-Clause Pause Ratio (ECPR)
Mid-Clause Pause Duration (MCPD)
End-Clause Pause Duration (ECPD)
Repair Fluency (RF) Disfluency Ratio

Thus, the following code block selects target measures. The code block also renames the columns filename and dysfluency_ratio to participant_id and disfluency_ratio, respectively.

df_uf_raw %>%
  select(
    filename,
    articulation_rate,
    mid_clause_pause_ratio,
    end_clause_pause_ratio,
    mid_clause_p.dur,
    end_clause_p.dur,
    dysfluency_ratio
  ) %>%
  rename(
    participant_id = filename,
    disfluency_ratio = dysfluency_ratio
  ) -> df_uf_tidy

df_uf_tidy

Next, the following code block loads data of post questionnaire about anxiety and linguistic background.

df_questionnaire_raw <- read.csv(
  here("data", "raw", "post_questionnaire.csv")
)

The following code block selects columns related to participant ID, anxiety, L2 English proficiency, and other backgrounds and renames them.

df_questionnaire_raw %>%
  select(
    参加者IDを入力してください.半角..,
    英語を話すとき.私は言葉を間違えてしまうのではとしばしば心配になる.,
    英語を話すとき.私は自分の話し方が他人より劣っているのではとしばしば心配になる.,
    英語を話し始めるとすぐに.私は自分自身のことを表現できないのではと心配になり始める.,
    英語を話すとき.私はドキドキすることがよくある.,
    英語を話すとき.私は緊張でびくびくすることがよくある.,
    英語を話すとき.私はよく汗をかいたり.発汗する.,
    英語スピーキングの練習をするとき.私はしばしば.すぐに投げ出してしまう.,
    私は英語スピーキングの練習の手を抜くことが多い.,
    私は普段.極力英語を話さないようにしている.,
    お持ちでしたら.英検のスコアを記入してください.,
    お持ちでしたら.IELTS..Overall..のスコアを記入してください.,
    お持ちでしたら.TOEFL.iBT.のスコアを記入してください.,
    お持ちでしたら.TOEIC.のスコアを記入してください.,
    性別,
    年齢
  ) %>%
  rename(
    participant_id = 参加者IDを入力してください.半角..,
    cognitive_anxiety_1 = 英語を話すとき.私は言葉を間違えてしまうのではとしばしば心配になる.,
    cognitive_anxiety_2 = 英語を話すとき.私は自分の話し方が他人より劣っているのではとしばしば心配になる.,
    cognitive_anxiety_3 = 英語を話し始めるとすぐに.私は自分自身のことを表現できないのではと心配になり始める.,
    somatic_anxiety_1 = 英語を話すとき.私はドキドキすることがよくある.,
    somatic_anxiety_2 = 英語を話すとき.私は緊張でびくびくすることがよくある.,
    somatic_anxiety_3 = 英語を話すとき.私はよく汗をかいたり.発汗する.,
    behavioral_anxiety_1 = 英語スピーキングの練習をするとき.私はしばしば.すぐに投げ出してしまう.,
    behavioral_anxiety_2 = 私は英語スピーキングの練習の手を抜くことが多い.,
    behavioral_anxiety_3 = 私は普段.極力英語を話さないようにしている.,
    IELTS = お持ちでしたら.IELTS..Overall..のスコアを記入してください.,
    TOEFL_IBT = お持ちでしたら.TOEFL.iBT.のスコアを記入してください.,
    TOEIC = お持ちでしたら.TOEIC.のスコアを記入してください.,
    eiken = お持ちでしたら.英検のスコアを記入してください.,
    sex = 性別,
    age = 年齢
  ) %>%
  mutate(
    sex = str_replace_all(sex, "男性", "male"),
    sex = str_replace_all(sex, "女性", "female"),
    eiken = str_replace_all(eiken, "準1級", "1.5"),
    eiken = str_replace_all(eiken, "準１級", "1.5"),
    eiken = str_replace_all(eiken, "2級", "2"),
    eiken = str_replace_all(eiken, "1級", "1"),
    eiken = str_replace_all(eiken, "英検4級", "4"),
    eiken = as.numeric(eiken)
  ) -> df_questionnaire_tidy

df_questionnaire_tidy

3. Preliminary Analysis

3.1. Participant Background

The following code block calculates the descriptive statistics of participants’ age.

df_questionnaire_tidy %>%
  select(age) %>%
  skim()
Data summary
Name Piped data
Number of rows 10
Number of columns 1
_______________________
Column type frequency:
numeric 1
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
age 0 1 28.8 5.61 20 26 29 30.5 38 ▅▅▇▂▅

The result showed that participants’ age was ranged \([20, 38]\), and their mean and SD were \(28.8\) and \(5.613\).

The following code block counts sex of participants.

df_questionnaire_tidy %>%
  group_by(sex) %>%
  summarize(N = n())

The result indicated that there were equal number of male and female participants.

3.2. Proficiency Levels

The following code block converts L2 English assessment scores to CEFR.

cefr_levels = c("A1", "A2", "B1", "B2", "C1", "C2")

df_questionnaire_tidy %>%
  select(participant_id, TOEFL_IBT, IELTS, TOEIC, eiken) %>%
  mutate(
    TOEFL_IBT = case_when(
      TOEFL_IBT >= 114 ~ "C2",
      TOEFL_IBT >= 95 ~ "C1",
      TOEFL_IBT >= 72 ~ "B2"
    ),
    IELTS = case_when(
      IELTS >= 7 ~ "C1"
    ),
    TOEIC = case_when(
      TOEIC >= 945 ~ "C1",
      TOEIC >= 785 ~ "B1",
      TOEIC >= 550 ~ "B2"
    ),
    eiken = case_when(
      eiken >= 3 ~ "A1",
      eiken >= 2 ~ "B1",
      eiken >= 1.5 ~ "B2",
      eiken >= 1 ~ "C1"
    )
  ) %>%
  mutate(
    TOEFL_IBT = factor(TOEFL_IBT, levels = cefr_levels, order = T),
    IELTS = factor(IELTS, levels = cefr_levels, order = T),
    TOEIC = factor(TOEIC, levels = cefr_levels, order = T),
    eiken = factor(eiken, levels = cefr_levels, order = T)
  ) %>% 
  replace_na(list(
    TOEFL_IBT = "A1",
    IELTS = "A1",
    TOEIC = "A1",
    eiken = "A1"
  )) %>%
  group_by(participant_id) %>%
  summarize(CEFR = max(TOEFL_IBT, IELTS, TOEIC, eiken)) %>%
  group_by(CEFR) %>%
  summarize(N = n())

The result suggested that most participants were advanced-level L2 English learners (\(N=6\)), while other four participants were intermediate-level English learners.

3.3. UF Measures

The following code block calculates the descriptive statistics of UF measures.

df_uf_tidy %>%
  select(-c(participant_id)) %>%
  skim()
Data summary
Name Piped data
Number of rows 10
Number of columns 6
_______________________
Column type frequency:
numeric 6
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
articulation_rate 0 1 3.81 0.69 2.70 3.37 3.70 4.24 4.90 ▂▇▇▂▅
mid_clause_pause_ratio 0 1 0.19 0.06 0.08 0.15 0.21 0.22 0.29 ▂▅▁▇▂
end_clause_pause_ratio 0 1 0.07 0.01 0.05 0.06 0.06 0.07 0.09 ▂▇▂▂▃
mid_clause_p.dur 0 1 0.76 0.26 0.44 0.58 0.69 0.89 1.25 ▇▆▁▂▃
end_clause_p.dur 0 1 0.83 0.25 0.49 0.65 0.77 1.06 1.19 ▅▇▂▂▇
disfluency_ratio 0 1 0.07 0.04 0.02 0.03 0.06 0.10 0.14 ▇▂▃▃▂

3.4. Speaking Anxiety

The following code blocks calculate the reliability of anxiety questionnaire answers in terms of Cronbach’s \(\alpha\).

3.4.1. Reliability of Cognitive Anxiety

df_questionnaire_tidy %>% 
  select(
    cognitive_anxiety_1,
    cognitive_anxiety_2,
    cognitive_anxiety_3
  ) %>%
  alpha()
## 
## Reliability analysis   
## Call: alpha(x = .)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N  ase mean  sd median_r
##       0.75      0.74    0.73      0.49 2.9 0.13  3.5 1.1      0.5
## 
##     95% confidence boundaries 
##          lower alpha upper
## Feldt     0.26  0.75  0.93
## Duhachek  0.49  0.75  1.00
## 
##  Reliability if an item is dropped:
##                     raw_alpha std.alpha G6(smc) average_r  S/N alpha se var.r
## cognitive_anxiety_1      0.81      0.83    0.71      0.71 4.89     0.11    NA
## cognitive_anxiety_2      0.65      0.66    0.50      0.50 1.97     0.21    NA
## cognitive_anxiety_3      0.42      0.42    0.27      0.27 0.73     0.37    NA
##                     med.r
## cognitive_anxiety_1  0.71
## cognitive_anxiety_2  0.50
## cognitive_anxiety_3  0.27
## 
##  Item statistics 
##                      n raw.r std.r r.cor r.drop mean  sd
## cognitive_anxiety_1 10  0.71  0.72  0.49   0.43  3.6 1.3
## cognitive_anxiety_2 10  0.81  0.81  0.72   0.60  3.7 1.3
## cognitive_anxiety_3 10  0.92  0.90  0.87   0.76  3.1 1.7
## 
## Non missing response frequency for each item
##                       1   2   3   4   5 miss
## cognitive_anxiety_1 0.0 0.3 0.1 0.3 0.3    0
## cognitive_anxiety_2 0.1 0.1 0.0 0.6 0.2    0
## cognitive_anxiety_3 0.2 0.3 0.0 0.2 0.3    0

The Cornbach’s \(\alpha\) of cognitive anxiety questionnaires was \(.747\), indicating an acceptable internal consistency

3.4.2. Reliability of Somatic Anxiety

df_questionnaire_tidy %>% 
  select(
    somatic_anxiety_1,
    somatic_anxiety_2,
    somatic_anxiety_3
  ) %>%
  alpha()
## 
## Reliability analysis   
## Call: alpha(x = .)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean  sd median_r
##        0.9       0.9    0.87      0.75 9.2 0.053  2.7 1.4     0.73
## 
##     95% confidence boundaries 
##          lower alpha upper
## Feldt     0.71   0.9  0.97
## Duhachek  0.80   0.9  1.00
## 
##  Reliability if an item is dropped:
##                   raw_alpha std.alpha G6(smc) average_r  S/N alpha se var.r
## somatic_anxiety_1      0.80      0.81    0.68      0.68  4.3     0.12    NA
## somatic_anxiety_2      0.84      0.84    0.73      0.73  5.3     0.10    NA
## somatic_anxiety_3      0.92      0.92    0.86      0.86 11.9     0.05    NA
##                   med.r
## somatic_anxiety_1  0.68
## somatic_anxiety_2  0.73
## somatic_anxiety_3  0.86
## 
##  Item statistics 
##                    n raw.r std.r r.cor r.drop mean  sd
## somatic_anxiety_1 10  0.94  0.94  0.92   0.87  2.9 1.5
## somatic_anxiety_2 10  0.94  0.92  0.89   0.83  2.8 1.7
## somatic_anxiety_3 10  0.86  0.88  0.76   0.73  2.5 1.4
## 
## Non missing response frequency for each item
##                     1   2   3   4   5 miss
## somatic_anxiety_1 0.2 0.3 0.1 0.2 0.2    0
## somatic_anxiety_2 0.3 0.2 0.2 0.0 0.3    0
## somatic_anxiety_3 0.3 0.3 0.0 0.4 0.0    0

The Cornbach’s \(\alpha\) of somatic anxiety questionnaires was \(.900\), indicating a excellent internal consistency.

3.4.3. Behavioral Anxiety

df_questionnaire_tidy %>% 
  select(
    behavioral_anxiety_1,
    behavioral_anxiety_2,
    behavioral_anxiety_3
  ) %>%
  alpha()
## 
## Reliability analysis   
## Call: alpha(x = .)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N ase mean  sd median_r
##       0.81       0.8    0.84      0.58 4.1 0.1  2.4 1.1     0.42
## 
##     95% confidence boundaries 
##          lower alpha upper
## Feldt     0.46  0.81  0.95
## Duhachek  0.61  0.81  1.01
## 
##  Reliability if an item is dropped:
##                      raw_alpha std.alpha G6(smc) average_r  S/N alpha se var.r
## behavioral_anxiety_1      0.53      0.55    0.38      0.38  1.2    0.283    NA
## behavioral_anxiety_2      0.58      0.59    0.42      0.42  1.4    0.260    NA
## behavioral_anxiety_3      0.97      0.97    0.94      0.94 30.8    0.021    NA
##                      med.r
## behavioral_anxiety_1  0.38
## behavioral_anxiety_2  0.42
## behavioral_anxiety_3  0.94
## 
##  Item statistics 
##                       n raw.r std.r r.cor r.drop mean  sd
## behavioral_anxiety_1 10  0.94  0.93  0.96   0.86  2.5 1.3
## behavioral_anxiety_2 10  0.93  0.91  0.95   0.81  2.8 1.4
## behavioral_anxiety_3 10  0.66  0.70  0.42   0.40  2.0 1.1
## 
## Non missing response frequency for each item
##                        1   2   3   4   5 miss
## behavioral_anxiety_1 0.2 0.4 0.2 0.1 0.1    0
## behavioral_anxiety_2 0.2 0.3 0.1 0.3 0.1    0
## behavioral_anxiety_3 0.4 0.3 0.2 0.1 0.0    0

The Cornbach’s \(\alpha\) of somatic anxiety questionnaires was \(.814\), indicating a good internal consistency.

3.5. Correlations

This subsection conducts correlation analyses between UF measures and speaking anxiety. Before the analyses, the following code block calculates three anxiety scores by summing items and joins the two dataframes.

df_questionnaire_tidy %>%
  group_by(participant_id) %>%
  summarize(
    cognitive_anxiety = sum(
      cognitive_anxiety_1, cognitive_anxiety_2, cognitive_anxiety_3
    ),
    somatic_anxiety = sum(
      somatic_anxiety_1, somatic_anxiety_2, somatic_anxiety_3
    ),
    behavioral_anxiety = sum(
      behavioral_anxiety_1, behavioral_anxiety_2, behavioral_anxiety_3
    )
  ) %>% 
  inner_join(
    df_uf_tidy, by = "participant_id"
  ) -> df_uf_anxiety

df_uf_anxiety

The following code block saves the concatenated dataframe as a csv file.

write.csv(df_uf_anxiety, here("data", "processed", "uf_anxiety.csv"))

3.5.1. Correlations Among Anxiety Scores

The following code block generates a correlation matrix of three anxiety scores.

df_uf_anxiety %>%
  select(
    cognitive_anxiety,
    somatic_anxiety,
    behavioral_anxiety
  ) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter

The result showed that significant strong correlation between cognitive and somatic anxiety (\(r=.78\)). In addition, there was slightly significant medium correlation between somatic and behavioral anxiety (\(r=.59\)). Meanwhile, there was small correlation between cognitive and behavioral anxiety (\(r=.48\)), but statistical significance was not found.

3.5.2. Correlations Between UF Measures and Cognitive Anxiety

The following code block generates a correlation matrix of UF measures and cognitive anxiety.

df_uf_anxiety %>%
  select(-c(
    participant_id, 
    somatic_anxiety, 
    behavioral_anxiety
  )) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter

The result showed significant large correlation between cognitive anxiety and ECPR, suggesting that participants produced end-clause pauses more frequently when cognitive anxiety was lower.

Moreover, scatter plots between cognitive anxiety and AR, MCPD, and ECPD demonstrated parabolic patterns. More specifically, AR was slower when cognitive anxiety was lower or higher. In contrast, MCPD and ECPD was longer when cognitive anxiety was lower or higher.

3.5.3. Correlations Between UF Measures and Somatic Anxiety

The following code block generates a correlation matrix of UF measures and somatic anxiety.

df_uf_anxiety %>%
  select(-c(
    participant_id, 
    cognitive_anxiety, 
    behavioral_anxiety
  )) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter

The result did not show significant correlations between somatic anxiety and UF measures.

3.5.4. Correlations Between UF Measures and Behavioral Anxiety

The following code block generates a correlation matrix of UF measures and behavioral anxiety.

df_uf_anxiety %>%
  select(-c(
    participant_id, 
    cognitive_anxiety, 
    somatic_anxiety
  )) %>%
  chart.Correlation(histogram = T, method = "pearson", pch = 19)
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter
## Warning in par(usr): argument 1 does not name a graphical parameter

The result identified significant large correlations between behavioral anxiety and MCPD (\(r=-.76\)) and ECPD (\(r=.79\)), suggesting that participants who perceived lower behavioral anxiety generate longer MCPD and ECPD.

4. Regression Analyses

4.1. Centralization

Given the parabolic relationship between cognitive anxiety and AR, MCPD, ECPD, I explore linear and quadratic relationship between them. To mitigate multicolinearity, the following code block centralizes anxiety scores.

df_uf_anxiety %>%
  mutate(
    cognitive_anxiety = cognitive_anxiety - mean(cognitive_anxiety),
    somatic_anxiety = somatic_anxiety - mean(somatic_anxiety),
    behavioral_anxiety = behavioral_anxiety - mean(behavioral_anxiety)
  ) -> df_uf_anxiety_centered

4.3. SF ~ Speaking Anxiety

Given the parabolic relationship between AR and cognitive anxiety, I compare linear and quadratic models in terms of AIC and the reliability of models.

4.3.1. Linear Model

The following code block constructs a linear model between AR and speaking anxiety, where cognitive anxiety term is a linear.

model_ar_linear <- lm(
  articulation_rate ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result.

tab_model(model_ar_linear, digits = 3, show.aic = T)
  articulation_rate
Predictors Estimates CI p
(Intercept) 3.814 3.198 – 4.431 <0.001
cognitive anxiety -0.036 -0.340 – 0.267 0.778
somatic anxiety -0.006 -0.276 – 0.265 0.962
behavioral anxiety 0.081 -0.172 – 0.333 0.464
Observations 10
R2 / R2 adjusted 0.104 / -0.344
AIC 28.729

The result did not show significant relationship between three anxiety scores and AR. In addition, AIC was \(28.729\).

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_ar_linear)

The results suggested that the linear model could be reliable.

4.2.2. Quadratic Model

The following code block constructs a quadratic model between AR and speaking anxiety, adding a quadratic cognitive anxiety term.

model_ar_quad <- lm(
  articulation_rate ~ cognitive_anxiety + I(cognitive_anxiety^2) + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result of the quadratic model.

tab_model(model_ar_quad, digits = 3, show.aic = T)
  articulation_rate
Predictors Estimates CI p
(Intercept) 3.392 1.893 – 4.891 0.002
cognitive anxiety 0.007 -0.349 – 0.364 0.960
cognitive anxiety^2 0.040 -0.086 – 0.166 0.455
somatic anxiety -0.064 -0.411 – 0.283 0.655
behavioral anxiety 0.190 -0.252 – 0.633 0.319
Observations 10
R2 / R2 adjusted 0.208 / -0.426
AIC 29.499

The result also showed that any anxiety did not significantly explain AR. AIC was \(29.499\), which was higher than the liner model, suggesting that the quadratic model is less-fit than the model linear.

The following code block conducts post-hoc analysis of the quadratic model.

check_model(model_ar_quad)

The results indicated that the quadratic model was less reliable because an outliner impact was big. Thus, I decided that the linear model is more representative of the association between AR and speaking anxiety though there was no significant relationship between them.

4.3. BDF ~ Speaking Anxiety

4.3.1. MCPR ~ Speaking Anxiety

The following code block constructs a regression model between MCPR and speaking anxiety.

model_mcpr <- lm(
  mid_clause_pause_ratio ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result.

tab_model(model_mcpr, digits = 3, show.aic = T)
  mid_clause_pause_ratio
Predictors Estimates CI p
(Intercept) 0.190 0.136 – 0.244 <0.001
cognitive anxiety 0.006 -0.020 – 0.033 0.580
somatic anxiety -0.000 -0.024 – 0.024 0.999
behavioral anxiety -0.000 -0.022 – 0.022 0.995
Observations 10
R2 / R2 adjusted 0.127 / -0.310
AIC -19.970

The result did not show significant relationship between three anxiety scores and MCPR.

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_mcpr)

The results suggested that the current model could be less reliable because the model could be affected by an outlier.

4.3.2. ECPR ~ Speaking Anxiety

The following code block constructs a regression model between ECPR and speaking anxiety.

model_ecpr <- lm(
  end_clause_pause_ratio ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result.

tab_model(model_ecpr, digits = 3, show.aic = T)
  end_clause_pause_ratio
Predictors Estimates CI p
(Intercept) 0.065 0.058 – 0.073 <0.001
cognitive anxiety -0.003 -0.007 – 0.001 0.081
somatic anxiety 0.001 -0.002 – 0.004 0.458
behavioral anxiety -0.001 -0.004 – 0.003 0.674
Observations 10
R2 / R2 adjusted 0.542 / 0.313
AIC -59.514

The result showed slightly significant relationship between cognitive anxiety and ECPR (\(p=.081\)). The slope was \(-.003\) and suggested that ECPR decreased \(.003\) when cognitive anxiety increased \(1\).

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_ecpr)

The results suggested that the current model could be reliable.

4.3.3. MCPD ~ Speaking Anxiety

Since the scatter plot showed parabolic relationship, I explore two linear and quadratic models.

4.3.3.1. Linear Model

The following code block constructs a linear model between MCPD and speaking anxiety.

model_mcpd_linear <- lm(
  mid_clause_p.dur ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result.

tab_model(model_mcpd_linear, digits = 3, show.aic = T)
  mid_clause_p.dur
Predictors Estimates CI p
(Intercept) 0.757 0.607 – 0.907 <0.001
cognitive anxiety -0.014 -0.088 – 0.060 0.655
somatic anxiety 0.026 -0.040 – 0.092 0.375
behavioral anxiety -0.074 -0.136 – -0.013 0.025
Observations 10
R2 / R2 adjusted 0.634 / 0.451
AIC 0.428

The result showed a significant link between behavioral anxiety and MCPD (\(p=.025\)). The slope was \(-.074\), suggesting that MCPD became \(.074\) shorter when behavioral anxiety score increased \(1\). In addition, AIC achieved \(.428\).

To examine the reliability of the linear model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_mcpd_linear)

The results suggested that the current model could be reliable.

4.3.3.2. Quadratic Model

The following code block constructs a quadratic model.

model_mcpd_quad <- lm(
  mid_clause_p.dur ~ cognitive_anxiety + I(cognitive_anxiety^2) + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block showed the result.

tab_model(model_mcpd_quad, digits = 3, show.aic = T)
  mid_clause_p.dur
Predictors Estimates CI p
(Intercept) 0.608 0.271 – 0.945 0.006
cognitive anxiety 0.001 -0.079 – 0.081 0.968
cognitive anxiety^2 0.014 -0.014 – 0.042 0.260
somatic anxiety 0.005 -0.073 – 0.083 0.873
behavioral anxiety -0.036 -0.135 – 0.064 0.397
Observations 10
R2 / R2 adjusted 0.723 / 0.502
AIC -0.373

The results did not demonstrate significant predictors, while AIC was \(-.373\), which was lower than the linear model.

The following code block conducts post-hoc analysis of the quadratic model.

check_model(model_mcpd_quad)

The results showed the model was affected by an outlier. Since the current sample size was 10, the lower AIC could be caused by overfit. Thus, I determined the linear model as a representative model.

4.3.4. ECPD ~ Speaking Anxiety

4.3.4.1. Linear model

The following code block constructs a linear model between AR and speaking anxiety.

model_ecpd_linear <- lm(
  end_clause_p.dur ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result.

tab_model(model_ecpd_linear, digits = 3, show.aic = T)
  end_clause_p.dur
Predictors Estimates CI p
(Intercept) 0.831 0.695 – 0.967 <0.001
cognitive anxiety -0.005 -0.072 – 0.062 0.872
somatic anxiety 0.017 -0.043 – 0.077 0.511
behavioral anxiety -0.072 -0.127 – -0.016 0.020
Observations 10
R2 / R2 adjusted 0.661 / 0.491
AIC -1.473

The result showed a significant link between behavioral anxiety and MCPD (\(p=.020\)). The slope was \(-.072\), suggesting that ECPD became \(.072\) shorter when behavioral anxiety score increased \(1\). AIC was \(-1.473\).

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_ecpd_linear)

The results suggested that the current model could be reliable.

4.3.4.2. Quadratic Model

The following code block constructs a linear model between AR and speaking anxiety.

model_ecpd_quad <- lm(
  end_clause_p.dur ~ cognitive_anxiety + I(cognitive_anxiety^2) + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result.

tab_model(model_ecpd_quad, digits = 3, show.aic = T)
  end_clause_p.dur
Predictors Estimates CI p
(Intercept) 0.783 0.436 – 1.129 0.002
cognitive anxiety 0.000 -0.082 – 0.083 0.990
cognitive anxiety^2 0.005 -0.025 – 0.034 0.704
somatic anxiety 0.010 -0.070 – 0.091 0.753
behavioral anxiety -0.059 -0.161 – 0.043 0.198
Observations 10
R2 / R2 adjusted 0.671 / 0.408
AIC 0.209

The result did not show significant predictor. Moreover, AIC was higher than the linear model (\(.209\)).

To examine the reliability of the quadratic model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_ecpd_quad)

The results suggested that the current model could be less reliable than the linear model because of larger outlier impacts.

4.4. RF ~ Speaking Anxiety

The following code block constructs a regression model between DR and speaking anxiety.

model_dr <- lm(
  disfluency_ratio ~ cognitive_anxiety + somatic_anxiety + behavioral_anxiety,
  df_uf_anxiety_centered
)

The following code block shows the result.

tab_model(model_dr, digits = 3, show.aic = T)
  disfluency_ratio
Predictors Estimates CI p
(Intercept) 0.067 0.028 – 0.107 0.006
cognitive anxiety 0.003 -0.016 – 0.022 0.712
somatic anxiety -0.003 -0.020 – 0.014 0.661
behavioral anxiety 0.003 -0.013 – 0.019 0.631
Observations 10
R2 / R2 adjusted 0.066 / -0.401
AIC -26.415

The result did not show significant relationship between three anxiety scores and DR.

To examine the reliability of the current model, the following code block conducts post-hoc analysis of regression assumptions.

check_model(model_dr)

The results suggested that the current model could be less reliable because the model could be affected by an outlier.